Abstract — The main goal of this article is to investigate the numerical solution of a vector-valued nonlinear wave equation, the nonlinearity being of the Ginzburg-Landau type, namely (|~u|2 − 1)~u. This equation is obtained when treating by penalty a constrained wave-motion, where the displacement vector is of constant length (1 here, after rescaling). An important step of the approximation p...

We carry out a rigorous error analysis of the first-order semi-discrete (in time) consistent splitting scheme coupled with generalized scalar auxiliary variable (GSAV) approach for Navier-Stokes equations no-slip boundary conditions. The is linear, unconditionally stable, and only requires solving sequence Poisson type at each time step. By using build-in unconditional stability GSAV approach, ...

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion...

This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each t...

Abstract A general framework for the development of high-order compact schemes has been proposed recently. The core steps are composed following. 1). Based on a kinetic model equation, from generalized initial distribution flow variables construct time-accurate evolution solution gas function at cell interface and obtain corresponding flux function; 2). Introduce WENO-type weighting functions i...

In recent years energy shortage and environmental impacts due to consuming fossil fuels have led to developing renewable energy sources systems. Since these sources are not reliable and are usually time dependent, an energy storing system like hydrogen production is required. In this regard, PEM electrolyzer can be efficiently used to decompose liquid water into hydrogen and oxygen. Because of ...